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Effect of flow topology on the kinetic energy flux in compressible isotropic turbulence

Published online by Cambridge University Press:  25 November 2019

Jianchun Wang Open the ORCID record for Jianchun Wang [Opens in a new window] ,
Minping Wan Open the ORCID record for Minping Wan [Opens in a new window] ,
Song Chen ,
Chenyue Xie Open the ORCID record for Chenyue Xie [Opens in a new window] ,
Qinmin Zheng ,
Lian-Ping Wang Open the ORCID record for Lian-Ping Wang [Opens in a new window]  and
Shiyi Chen
Jianchun Wang*
Affiliation:
Shenzhen Key Laboratory of Complex Aerospace Flows, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
Minping Wan
Affiliation:
Shenzhen Key Laboratory of Complex Aerospace Flows, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
Song Chen
Affiliation:
Shenzhen Key Laboratory of Complex Aerospace Flows, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
Chenyue Xie
Affiliation:
Shenzhen Key Laboratory of Complex Aerospace Flows, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
Qinmin Zheng
Affiliation:
Shenzhen Key Laboratory of Complex Aerospace Flows, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
Lian-Ping Wang
Affiliation:
Shenzhen Key Laboratory of Complex Aerospace Flows, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA
Shiyi Chen*
Affiliation:
Shenzhen Key Laboratory of Complex Aerospace Flows, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing 100871, PR China
*
†Email addresses for correspondence: wangjc@sustech.edu.cn, chensy@sustech.edu.cn
†Email addresses for correspondence: wangjc@sustech.edu.cn, chensy@sustech.edu.cn
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Abstract

The effects of flow topology on the subgrid-scale (SGS) kinetic energy flux in compressible isotropic turbulence is studied. The eight flow topological types based on the three invariants of the filtered velocity gradient tensor are analysed at different scales, along with their roles in the magnitude and direction of kinetic energy transfer. The unstable focus/compressing (UFC), unstable node/saddle/saddle (UN/S/S) and stable focus/stretching (SFS), are the three predominant topological types at all scales; they account for at least 75 % of the flow domain. The UN/S/S and SFS types make major contributions to the average SGS flux of the kinetic energy from large scales to small scales in the inertial range. The unstable focus/stretching (UFS) topology makes a contribution to the reverse SGS flux of kinetic energy from small scales to large scales. In strong compression regions, the average contribution of the stable node/saddle/saddle (SN/S/S) topology to the SGS kinetic energy flux is positive and is predominant over those of other flow topologies. In strong expansion regions, the UFS topology makes a major contribution to the reverse SGS flux of the kinetic energy. As the turbulent Mach number increases, the increase of volume fraction of the UFS topological regions leads to the increase of the SGS backscatter of kinetic energy. The SN/S/S topology makes a dominant contribution to the direct SGS flux of the compressible component of the kinetic energy, while the UFS topology makes a dominant contribution to the reverse SGS flux of the compressible component of the kinetic energy.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A11
Copyright
© 2019 Cambridge University Press

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References

Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106, 174502.CrossRefGoogle ScholarPubMed
Aluie, H. 2013 Scale decomposition in compressible turbulence. Physica D 247, 54–65.CrossRefGoogle Scholar
Aluie, H. & Eyink, G. L. 2009 Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter. Phys. Fluids 21, 115108.CrossRefGoogle Scholar
Aluie, H., Li, S. & Li, H. 2012 Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751, L29.CrossRefGoogle Scholar
Balsara, D. S. & Shu, C. W. 2000 Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comput. Phys. 160, 405–452.CrossRefGoogle Scholar
Blackburn, H. M., Mansour, N. N. & Cantwell, B. J. 1996 Topology of fine scale motions in turbulent channel flow. J. Fluid Mech. 310, 269–292.CrossRefGoogle Scholar
Bechlars, P. & Sandberg, R. D. 2017a Evolution of the velocity gradient tensor invariant dynamics in a turbulent boundary layer. J. Fluid Mech. 815, 223–242.CrossRefGoogle Scholar
Bechlars, P. & Sandberg, R. D. 2017b Variation of enstrophy production and strain rotation relation in a turbulent boundary layer. J. Fluid Mech. 812, 321–348.CrossRefGoogle Scholar
Borue, V. & Orszag, S. A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31.CrossRefGoogle Scholar
van der Bos, F., Tao, B., Meneveau, C. & Katz, J. 2002 Effects of small-scale turbulent motions on the filtered velocity gradient tensor as deduced from holographic particle image velocimetry measurements. Phys. Fluids 14, 2456–2474.CrossRefGoogle Scholar
Boschung, J., Schaefer, P., Peters, N. & Meneveau, C. 2014 The local topology of stream- and vortex lines in turbulent flows. Phys. Fluids 26, 045107.CrossRefGoogle Scholar
Chacin, J. M. & Cantwell, B. J. 2000 Dynamics of a low Reynolds number turbulent boundary layer. J. Fluid Mech. 404, 87–115.CrossRefGoogle Scholar
Chertkov, M., Pumir, A. & Shraiman, B. I. 1999 Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11, 2394–2410.CrossRefGoogle Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765–777.CrossRefGoogle Scholar
Chong, M. S., Soria, J., Perry, A. E., Chacin, J., Cantwell, B. J. & Na, Y. 1998 Turbulence structures of wall bounded shear flows found using DNS data. J. Fluid Mech. 357, 225–247.CrossRefGoogle Scholar
Chu, Y. B. & Lu, X. Y. 2013 Topological evolution in compressible turbulent boundary layers. J. Fluid Mech. 733, 414–438.CrossRefGoogle Scholar
Cifuentes, L., Dopazo, C., Martin, J. & Jimenez, C. 2014 Local flow topologies and scalar structures in a turbulent premixed flame. Phys. Fluids 26, 065108.CrossRefGoogle Scholar
Cifuentes, L., Dopazo, C., Martin, J., Domingo, P. & Vervisch, L. 2016 Effects of the local flow topologies upon the structure of a premixed methane-air turbulent jet flame. Flow Turbul. Combust. 96, 535–546.CrossRefGoogle Scholar
Dai, Q., Luo, K., Jin, T. & Fan, J. 2017 Direct numerical simulation of turbulence modulation by particles in compressible isotropic turbulence. J. Fluid Mech. 832, 438–482.CrossRefGoogle Scholar
Danish, M. & Meneveau, C. 2018 Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence. Phys. Rev. Fluids 3, 044604.CrossRefGoogle Scholar
Danish, M., Sinha, S. S & Srinivasan, B. 2016a Influence of compressibility on the Lagrangian statistics of vorticity-strain-rate interactions. Phys. Rev. E 94, 013101.CrossRefGoogle Scholar
Danish, M., Suman, S. & Girimaji, S. S 2016b Influence of flow topology and dilatation on scalar mixing in compressible turbulence. J. Fluid Mech. 793, 633–655.CrossRefGoogle Scholar
Duraisamy, K., Iaccarino, G. & Xiao, H. 2019 Turbulence modeling in the age of data. Annu. Rev. Fluid Mech. 51, 357–377.CrossRefGoogle Scholar
Elsinga, G. E. & Marusic, I. 2010 Universal aspects of small-scale motions in turbulence. J. Fluid Mech. 662, 514–539.CrossRefGoogle Scholar
Eyink, G. L. 2005 Locality of turbulent cascades. Physica D 207, 91–116.Google Scholar
Eyink, G. L. & Aluie, H. 2009 Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining. Phys. Fluids 21, 115107.CrossRefGoogle Scholar
Gamahara, M. & Hattori, Y. 2017 Searching for turbulence models by artificial neural network. Phys. Rev. Fluids 2, 054604.CrossRefGoogle Scholar
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2007 Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592, 335–366.CrossRefGoogle Scholar
Jagannathan, S. & Donzis, D. A. 2016 Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations. J. Fluid Mech. 789, 669–707.CrossRefGoogle Scholar
Johnson, P. L. & Meneveau, C. 2017 Turbulence intermittency in a multiple-time-scale Navier–Stokes-based reduced model. Phys. Rev. Fluids 2, 072601(R).CrossRefGoogle Scholar
Kumari, K., Mahapatra, S., Ghosh, S. & Mathew, J. 2018 Invariants of velocity gradient tensor in supersonic turbulent pipe, nozzle, and diffuser flows. Phys. Fluids 30, 015104.CrossRefGoogle Scholar
Lai, J., Wacks, D. H. & Chakraborty, N. 2018 Flow topology distribution in head-on quenching of turbulent premixed flame: a direct numerical simulation analysis. Fuel 224, 186–209.CrossRefGoogle Scholar
Ling, J., Jones, R. & Templeton, J. 2016a Machine learning strategies for systems with invariance properties. J. Comput. Phys. 318, 22–35.CrossRefGoogle Scholar
Ling, J., Kurzawski, A. & Templeton, J. 2016b Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. 807, 155–166.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Lozano-Durán, A., Holzner, M. & Jiménez, J. 2016 Multiscale analysis of the topological invariants in the logarithmic region of turbulent channels at a friction Reynolds number of 932. J. Fluid Mech. 803, 356–394.CrossRefGoogle Scholar
Lüthi, B., Ott, S., Berg, J. & Mann, J. 2007 Lagrangian multi-particle statistics. J. Turbul. 8, 1–17.Google Scholar
Martin, M. P., Piomelli, U. & Candler, G. V. 2000 Subgrid-scale models for compressible large-eddy simulations. J. Theor. Comput. Fluid Dyn. 13, 361–376.Google Scholar
Mathew, J., Ghosh, S. & Friedrich, R. 2016 Changes to invariants of the velocity gradient tensor at the turbulentšCnonturbulent interface of compressible mixing layers. Intl J. Heat Fluid Flow 59, 125–130.CrossRefGoogle Scholar
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245.CrossRefGoogle Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.CrossRefGoogle Scholar
Mishra, A. A. & Girimaji, S. S. 2015 Hydrodynamic stability of three-dimensional homogeneous flow topologies. Phys. Rev. E 92, 053001.Google ScholarPubMed
Naso, A. & Pumir, A. 2005 Scale dependence of the coarse-grained velocity derivative tensor structure in turbulence. Phys. Rev. E 72, 056318(R).Google ScholarPubMed
Naso, A., Chertkov, M. & Pumir, A. 2006 Scale dependence of the coarse-grained velocity derivative tensor: influence of large-scale shear on small-scale turbulence. J. Turbul. 7, 1–11.Google Scholar
Naso, A., Pumir, A. & Chertkov, M. 2007 Statistical geometry in homogeneous and isotropic turbulence. J. Turbul. 8, 1–13.Google Scholar
Nomura, K. K. & Diamessis, P. J. 2000 The interaction of vorticity and rate-of-strain in homogeneous sheared turbulence. Phys. Fluids 12, 846–864.CrossRefGoogle Scholar
Ooi, A., Martin, J., Soria, J. & Chong, M. S. 1999 A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141–174.CrossRefGoogle Scholar
Papapostolou, V., Wacks, D. H., Chakraborty, N., Klein, M. & Im, H. G. 2017 Enstrophy transport conditional on local flow topologies in different regimes of premixed turbulent combustion. Sci. Rep. UK 7, 11545.Google ScholarPubMed
Pan, S. & Johnsen, E. 2017 The role of bulk viscosity on the decay of compressible, homogeneous, isotropic turbulence. J. Fluid Mech. 833, 717–744.CrossRefGoogle Scholar
Parashar, N., Sinha, S. S., Danish, M. & Srinivasan, B. 2017 Lagrangian investigations of vorticity dynamics in compressible turbulence. Phys. Fluids 29, 105110.CrossRefGoogle Scholar
Pirozzoli, S. & Grasso, F. 2004 Direct numerical simulations of isotropic compressible turbulence: influence of compressibility on dynamics and structures. Phys. Fluids 16, 4386–4407.CrossRefGoogle Scholar
Pumir, A. & Naso, A. 2010 Statistical properties of the coarse-grained velocity gradient tensor in turbulence: Monte-Carlo simulations of the tetrad model. New J. Phys. 12, 123024.Google Scholar
Quadros, R., Sinha, K. & Larsson, J. 2016 Turbulent energy flux generated by shock/homogeneous-turbulence interaction. J. Fluid Mech. 796, 113–157.CrossRefGoogle Scholar
Ryu, J. & Livescu, D. 2014 Turbulence structure behind the shock in canonical shock-vortical turbulence interaction. J. Fluid Mech. 756, R1.CrossRefGoogle Scholar
Samtaney, R., Pullin, D. I. & Kosovic, B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13, 1415–1430.CrossRefGoogle Scholar
Sciacovelli, L., Cinnella, P. & Grasso, F. 2017 Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence. J. Fluid Mech. 825, 515–549.CrossRefGoogle Scholar
da Silva, C. B. & Pereira, J. C. F. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20, 055101.CrossRefGoogle Scholar
Soria, J., Sondergaard, R., Cantwell, B. j, Chong, M. S. & Perry, A. E. 1994 A study of the fine-scale motions of incompressible time-developing mixing layers. Phys. Fluids 6, 871–884.CrossRefGoogle Scholar
Suman, S. & Girimaji, S. S. 2010 Velocity gradient invariants and local flow-field topology in compressible turbulence. J. Turbul. 11, 1–24.Google Scholar
Vaghefi, N. S. & Madnia, C. K. 2015 Local flow topology and velocity gradient invariants in compressible turbulent mixing layer. J. Fluid Mech. 774, 67–94.CrossRefGoogle Scholar
Wacks, D. & Chakraborty, N. 2016a Flow topology and alignments of scalar gradients and vorticity in turbulent spray flames: a direct numerical simulation analysis. Fuel 184, 922–947.CrossRefGoogle Scholar
Wacks, D. H., Chakraborty, N. & Klein, M. 2016b Flow topologies in different regimes of premixed turbulent combustion: a direct numerical simulation analysis. Phys. Rev. Fluids 1, 083401.CrossRefGoogle Scholar
Wacks, D., Konstantinou, L. & Chakraborty, N. 2018 Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames. Proc. R. Soc. Lond. A 474, 20170706.CrossRefGoogle ScholarPubMed
Wang, J., Gotoh, T. & Watanabe, T. 2017a Spectra and statistics in compressible isotropic turbulence. Phys. Rev. Fluids 2, 013403.Google Scholar
Wang, J., Gotoh, T. & Watanabe, T. 2017b Shocklet statistics in compressible isotropic turbulence. Phys. Rev. Fluids 2, 023401.Google Scholar
Wang, J., Gotoh, T. & Watanabe, T. 2017c Scaling and intermittency in compressible isotropic turbulence. Phys. Rev. Fluids 2, 053401.Google Scholar
Wang, J., Shi, Y., Wang, L.-P., Xiao, Z., He, X. T. & Chen, S. 2011 Effect of shocklets on the velocity gradients in highly compressible isotropic turbulence. Phys. Fluids 23, 125103.CrossRefGoogle Scholar
Wang, J., Shi, Y., Wang, L.-P., Xiao, Z., He, X. T. & Chen, S. 2012 Effect of compressibility on the small scale structures in isotropic turbulence. J. Fluid Mech. 713, 588–631.CrossRefGoogle Scholar
Wang, J., Wan, M., Chen, S. & Chen, S. Y. 2018a Kinetic energy transfer in compressible isotropic turbulence. J. Fluid Mech. 841, 581–613.CrossRefGoogle Scholar
Wang, J., Wan, M., Chen, S., Xie, C. & Chen, S. Y. 2018b Effect of shock waves on the statistics and scaling in compressible isotropic turbulence. Phys. Rev. E 97, 043108.CrossRefGoogle Scholar
Wang, J., Wan, M., Chen, S., Xie, C., Wang, L.-P. & Chen, S. Y. 2019 Cascades of temperature and entropy fluctuations in compressible turbulence. J. Fluid Mech. 867, 195–215.CrossRefGoogle Scholar
Wang, J., Wang, L.-P., Xiao, Z., Shi, Y. & Chen, S. 2010 A hybrid numerical simulation of isotropic compressible turbulence. J. Comput. Phys. 229, 5257–5279.CrossRefGoogle Scholar
Wang, J., Yang, Y., Shi, Y., Xiao, Z., He, X. T. & Chen, S. 2013 Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett. 110, 214505.CrossRefGoogle ScholarPubMed
Wang, L. & Lu, X. Y. 2012 Flow topology in compressible turbulent boundary layer. J. Fluid Mech. 703, 255–278.CrossRefGoogle Scholar
Wang, Z., Luo, K., Li, D., Tan, J. & Fan, J. 2018 Investigations of data-driven closure for subgrid-scale stress in large-eddy simulation. Phys. Fluids 30, 125101.CrossRefGoogle Scholar
Xie, C., Wang, J., Li, K. & Ma, C. 2019 Artificial neural network approach to large-eddy simulation of compressible isotropic turbulence. Phys. Rev. E 99, 053113.Google ScholarPubMed
Yang, Y., Wang, J., Shi, Y., Xiao, Z., He, X. T. & Chen, S. 2016 Intermittency caused by compressibility: a Lagrangian study. J. Fluid Mech. 786, R6.CrossRefGoogle Scholar
Zhou, Y., Nagata, K., Sakai, Y., Ito, Y. & Hayase, T. 2015 On the evolution of the invariants of the velocity gradient tensor in single-square-grid-generated turbulence. Phys. Fluids 27, 075107.CrossRefGoogle Scholar